hw6 - CALCULUS 1501 WINTER 2010 HOMEWORK ASSIGNMENT 6. Due...

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HOMEWORK ASSIGNMENT 6. Due February 26. 6.1. Determine whether the series
∞ n=1 ∞ n2 1 + 5n + 6 is convergent or divergent. If it is convergent, ﬁnd its sum. 6.2. Find the value of c such that
n=1 ∞ 2nc = 2010. an is Sn = 3 − n2−n , ﬁnd an and
n=1 ∞ n=1 an . 6.3. If the n-th partial sum of a series
∞ 6.4. Let
n=1 an be a series with positive terms.
∞ (a) Suppose that for any n ≥ 1, the partial sum Sn satisﬁes Sn < 100. Prove that converges. (b) Suppose that for any n ≥ 1, an <
∞ n=1 an 1 2 n . Prove that
n=1 an converges. In both parts, you do not need to ﬁnd the sum of the series. 1 ...
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